论文标题
基于高斯流程的随机衍生信任区域方法的收敛证书
Convergence Certificate for Stochastic Derivative-Free Trust-Region Methods based on Gaussian Processes
论文作者
论文摘要
在许多机器学习应用程序中，人们希望从可用数据中学习优化问题的未知目标和约束功能，然后应用一些技术来获得学习模型的本地优化器。这项工作将高斯流程视为全球替代模型，并与无衍生的信任区域方法一起利用它们。众所周知，如果替代模型在概率上是完全线性的，那么无衍生的信任区域方法在全球范围内收敛。我们证明\ glspl {gp}确实是概率完全线性的，因此导致快速（与线性或二次局部替代模型相比）和全局收敛。我们利用化学反应器的优化来证明\ gls {gp}基于信任区域的效率。
In many machine learning applications, one wants to learn the unknown objective and constraint functions of an optimization problem from available data and then apply some technique to attain a local optimizer of the learned model. This work considers Gaussian processes as global surrogate models and utilizes them in conjunction with derivative-free trust-region methods. It is well known that derivative-free trust-region methods converge globally---provided the surrogate model is probabilistically fully linear. We prove that \glspl{gp} are indeed probabilistically fully linear, thus resulting in fast (compared to linear or quadratic local surrogate models) and global convergence. We draw upon the optimization of a chemical reactor to demonstrate the efficiency of \gls{gp}-based trust-region methods.
